Problem: Express this product in scientific notation: $(3.50\times 10^{-3})\times (3.00\times 10^{-5})$
Start by collecting like terms together. $= (3.50\times 3.00) \times (10^{-3}\times 10^{-5})$ When multiplying exponents with the same base, add the powers together. $= 10.5 \times 10^{-3\,+\,-5}$ $= 10.5 \times 10^{-8}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $10.5$ is the same as $1.050 \times 10$ $ = {1.050 \times 10} \times 10^{-8} $ $= 1.050\times 10^{-7}$